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- [Instructor] Elsewhere in this course,
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I have described how to enumerate
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the number of possibilities through permutations
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when the order of things matters.
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In this movie, I will describe combinations
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where order doesn't matter.
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As an example, assume that you have five products
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and you draw from them to create gift baskets
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or samples for potential customers.
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So the question is, if you had five items
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and you take three, and you do not allow duplication,
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how many possible different combinations do you have?
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And once again, combinations must occur without duplication.
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However, in contrast to permutations,
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order doesn't matter.
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A gift basket with these three items
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would be the same as a gift basket with the same items,
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even if they were put into the basket in a different order.
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So our goal is to calculate how many unique groups
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are possible when choosing three or five products
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without allowing repetition.
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To demonstrate, I will switch over to Excel.
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I have opened this movie's Excel sample file,
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and it is 06_06 Combinations Without Duplication.
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You can find that in the chapter six folder
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of the exercise files collection.
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This is a fairly straightforward workbook,
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and you can see that I only need two pieces of data,
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those are in B-3 and B-4.
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Those are the number of available products in B-3,
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and the number of items in a sample basket in B-4.
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So I'll click in cell B-6,
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and I'll create my first formula,
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type an equal sign,
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and I want to find the number of combinations.
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So in other words, because order doesn't matter,
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I can use combinations, rather than permutations.
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So I'll make sure that I have COMBIN
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entered into the formula,
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and B-3 contains the number
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that is the number of potential items
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from which we will select, then a comma,
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and the number chosen
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that's before the items in each basket.
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Write parenthesis and Enter,
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and I see that there are 10 possible combinations.
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If I increased the number of available products
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from five to eight,
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we would go from 10 to 56 possible combinations.
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And if I wanted to increase the number of items
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in the basket from three to four,
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still leaving eight available,
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we would go from 56 to 70.
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Because order doesn't matter with combinations
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like it does for permutations,
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the number of possible combinations increases more slowly
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than does the number of possible permutations.
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However, I guarantee that as the number
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of available products
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and the number of items in the sample basket grow,
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the number of combinations will grow very quickly.
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